Fuzzy elements in a fuzzy set

Didier Dubois (1) , Henri Prade (2)

1 UT3 - Université Toulouse III - Paul Sabatier
2 IRIT-ADRIA - Argumentation, Décision, Raisonnement, Incertitude et Apprentissage

This paper introduces a new concept in fuzzy set theory, that of a fuzzy element. It embodies the idea of fuzziness only, thus contributing to the distinction between fuzziness and ideas of imprecision. A fuzzy element is to a fuzzy set what an element is to a set. A fuzzy element is as precise as an element, just more gradual that the latter. Applications of this notion to fuzzy cardinality, fuzzy interval analysis and defuzzification principles are outlined.

Mots clés: Fuzzy set; alpha-cuts; fuzzy numbers

Domaines: Intelligence artificielle [cs.AI]

Didier Dubois, Henri Prade. Fuzzy elements in a fuzzy set. International Fuzzy Systems Association World Congress, Jul 2005, Beijing, China. pp.55--60. ⟨hal-03367408⟩